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arXiv · 2509.02380

Faster Algorithms for the Least-Core value and the Nucleolus in Convex Games

Giacomo Maggiorano·Alessandro Sosso·Gautier Stauffer
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Abstract

The nucleolus is a central solution concept in cooperative game theory. While its computation is NP-hard in general, it can be computed in polynomial time for convex games; however, the only published polynomial-time algorithm relies on the ellipsoid method. We develop a combinatorial alternative based on reduced games and iterative least-core value computations. Leveraging submodular function minimization and polyhedral structure in a novel way, we obtain a faster combinatorial algorithm for computing the least-core value, improving the oracle complexity by a factor $n^3$ over previous approaches. As a consequence, we obtain a new strongly polynomial-time and combinatorial algorithm for computing the nucleolus in convex games. Preliminary analysis indicates an improved oracle complexity compared to the ellipsoid-based algorithm.

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Giacomo Maggiorano, Alessandro Sosso, Gautier Stauffer. 2025-09-02. Faster Algorithms for the Least-Core value and the Nucleolus in Convex Games. https://arxiv.org/abs/2509.02380

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